
The Input module
3 | C_4,2
4 | C_1,3|4
5 | C_1,2|4
6 | C_3,2|4,1
For a detailed use of the function uq_CopulaSummary, see Section 3.8.5.
Additionally, a graph of the vine’s constituting pair copulas and edges among them, such as
those shown in Figure 3, can be visualized using the function uq_drawVineCopula.
2.1.2.4 Truncated vines
As discussed in Section 1.4.4, the higher-order dependencies needed for the construction of
a vine copula may be difficult to assert, or to reliably infer from data. Also, when setting the
vine structure such that pair copulas among more strongly correlated random variables are
captured in earlier trees, higher-order dependencies play a less significant role in shaping the
joint PDF and can often be neglected. This is also the approach taken by UQLAB and by most
software when inferring vine copulas from data (see the UQLAB User Manual – Statistical
inference, Section 1.3.3).
Representing a vine truncated at tree t is possible by using the additional code
Input.Copula.Truncation = t;
for any t = 1, . . . , M, where t = 1 sets all pair copulas to the independence pair copula,
and thus the vine to the independence M-copula, and t = M corresponds to no truncation.
Values of t lower than 1 or larger than M are also interpreted by UQLAB as no truncation.
Note: For a vine truncated at level t, only the pair copulas in the first t − 1 trees need
to be specified. The others are by definition the independence copula.
Since the j-th tree contains M −j copulas, a total of (M −1) + (M −2) + . . . + (M −t −1) =
(t − 1)M − t(t + 1)/2 are to be defined (see Table 3 for the number of non-truncated pair
copulas in a vine for different values of M and t). UQLAB additionally handles several special
cases as follows:
• an error is thrown if not enough or too many pair copulas are specified (for instance, if
M = 10, t = 3 and less than 17 or more than 45 pair copulas are provided);
• a warning is given if more pair copulas than the non-truncated ones are specified (for
instance, if M = 10, t = 3 and more than 17 pair copulas are provided).
2.1.3 Independent subgroups of random variables
As mentioned in Section 1.3.2, the copula of a random vector consisting of independent
subgroups of random variables is given by the product of the copulas of all subgroups (see
(1.8) for the case d = 2). Subgroup independence can be specified in UQLAB by simply
defining any number of input copulas, and the variables associated to each one. The full
copula is automatically understood to be the tensor product of the individual copulas. For
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